{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 第五章　组合优化与模拟退火方法\n",
    "\n",
    "\n",
    "作者：[王何宇](http://person.zju.edu.cn/wangheyu)\n",
    "\n",
    "[浙江大学数学科学学院](http://www.math.zju.edu.cn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这一章我们将不再继续学习如何抽样，而是开始用学到的技术去解决实际优化问题。这里的优化主要指组合优化，尽管我们即将提到的这些方法，对于一些连续优化中的困难情形，如多目标优化等等，也有一定的作用。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 组合优化问题的描述\n",
    "我们知道有很多离散优化问题，是属于NP（Non-deterministic Polynomial ）的，其中最著名的一个可能就是 TSP（Traveling Salesman Problem）问题，它的一种描述如下：给定$n$ 个城市和每两个城市间的距离（无向完全图，有权边），选择一条线路，使得每个城市只经过一次且仅有一次，并最终回到起点。求能完成这个遍历的总路径长度最短。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于完全图，我们用邻接矩阵（adjacency matrix）$D = [d_{ij}]$ 来表示全部城市，其中 $d_{ij}$ 表示城市 $i$ 和 $j$ 之间的距离。显然，$d_{ij}$满足：\n",
    "+ $d_{ij} \\geq 0, 1 \\leq i, j \\leq n$;\n",
    "+ $d_{ii} = 0, 1 \\leq i \\leq n$;\n",
    "+ $d_{ij} = d_{ji}, 1 \\leq i, j \\leq n$;\n",
    "+ $d_{ij} + d_{jk} \\geq d_{ik}, 1 \\leq i, j, k \\leq n$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "而问题的一个解可以表达为一个循环排列\n",
    "$$\n",
    "\\pi = (\\pi_1, \\pi_2, \\cdots, \\pi_n),\n",
    "$$\n",
    "表示路径\n",
    "$$\n",
    "\\pi_1 \\to \\pi_2 \\to \\cdots \\to \\pi_n,\n",
    "$$\n",
    "其中 $\\pi_i \\in \\{1, 2, \\cdots, n\\}, i = 1, 2, \\cdots, n$ 表示各个城市的编号，显然对可行解，有 $i \\neq j$，则 $\\pi_i \\neq \\pi_j$。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "若记 $S$ 为全体可行解，则易知\n",
    "$$\n",
    "\\begin{equation}\n",
    "  |S| = \\frac{(n - 1)!}{2}.\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "这是一个随 $n$ 增加指数增长的数值，因此对于较大的 $n$ 不太可能用遍历穷举的方式来寻找最优解。这里目标函数可以表示为\n",
    "$$\n",
    "\\begin{equation}\n",
    "  f(\\pi) = \\sum_{i = 1}^n d_{\\pi_i, \\pi_{i + 1}},\n",
    "\\end{equation}\n",
    "$$\n",
    "并约定 $\\pi_{n + 1} = \\pi_1$。\n",
    "\n",
    "于是整个优化问题按组合优化的约定，可以表达为\n",
    "$$\n",
    "\\begin{equation}\n",
    "  \\min f(\\pi_i), \\pi_i \\in S.\n",
    "\\label{eq::TSP_opt}\n",
    "\\end{equation}\n",
    "$$\n",
    "而此优化问题的解则定义为："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**全局最优解** 称 $\\pi^* \\in S$ 为 TSP 问题的全局最优解，或简称最优解，若 $\\forall \\pi_i \\in S$，有\n",
    "$$\n",
    "f(\\pi^*) \\leq f(\\pi_i).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "作为一个典型的 NP 问题，对每一个可行解（存在的路径），我们都可以迅速得到总路径长度（多项式时间）。然而，求最短路径本身却至今没有什么太好的确定性算法。在这种情况下，随机搜索算法被提到桌面上讨论。然而现在出现新的困难，最优解是一个非常孤立的偶然事件，同时分布上也\n",
    "没有明显的规律（或者我们无法先验地获知它的分布情况），如果完全在 $S$ 全空间随机投点，去碰一个偶然事件，那么收敛速度甚至收敛性本身都很有问题。针对这种未知分布的情况，之前的 Metropolis-Hasting 抽样给我们一定的启示。但首先，我们先观察一下 $S$ 的结构（总是要尽可能获取背景信息）。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**$2$-变换邻域** 对于$S$中的一个解\n",
    "$$\n",
    "\\pi = \\{\\pi_1, \\pi_2, \\cdots, \\pi_{p - 1}, \\pi_p, \\pi_{p + 1},\n",
    "\\cdots, \\pi_{q - 1}, \\pi_q, \\pi_{q + 1}, \\cdots, \\pi_n\\},\n",
    "$$\n",
    "称\n",
    "$$\n",
    "N_2(p, q): \\pi \\to \\pi', p < q\n",
    "$$\n",
    "为 $2$-变换，如果\n",
    "$$\n",
    "\\pi'= \\{\\pi_1, \\pi_2, \\cdots, \\pi_{p - 1}, \\pi_q, \\pi_{q - 1},\n",
    "\\cdots, \\pi_{p + 1}, \\pi_p, \\pi_{q + 1}, \\cdots, \\pi_n\\}.\n",
    "$$\n",
    "这里 $\\forall \\pi_i \\in S$，称 $S_i$ 为 $\\pi_i$ 的 $2$-变换邻域，若 $S_i \\subseteq S$，且 $\\forall \\pi_j \\in S_i$，$\\pi_j$ 可由 $\\pi_i$ 经一次 $2$-变换得到。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "类似的，我们还可以定义 $k$-变换，以及 $k$-变换邻域。但注意到 $\\forall i, j \\in S$，我们都可以用至多 $n - 2$ 次 $2$-变换将二者互换（可遍历）。所以从考虑可行解之间关系角度，$2$-变换在很多场合也够用了。有了邻域，我们可以进一步提出：\n",
    "\n",
    "**局部最优解** 记 $\\pi^* \\in S$ 的邻域为 $S^*$，若 $\\forall \\pi_i \\in S^*$，有\n",
    "$$\n",
    "f(\\pi_i) \\geq f(\\pi^*), \n",
    "$$\n",
    "则称 $\\pi^*$ 为 TSP 问题的局部最优解。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在我们给出一个用于求解一般组合优化问题的伪代码：\n",
    "```\n",
    "def local_search(i0):\n",
    "    i = i0\n",
    "    while (i不是局部最优解):\n",
    "        从i的邻域Si中选取一个可行解j\n",
    "        if f(j) < f(i):\n",
    "            i = j\n",
    "    return i\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这个算法很没用。它只能提供局部最优解，而 TSP 问题显然要求的是全局最优解或尽可能接近全局最优解。（TSP 算法有实用的离散算法，详见谈之奕老师主讲课程《组合优化》。）我们这里考虑能否使用随机搜索的手段，使这个算法摆脱局部最优解的困扰，但同时我们又要利用局部最优性。因为在没有其他任何信息的时候，局部最优性显然提供了一个邻域内的有效索方向。这里可以考虑的几个关键点是：\n",
    "\n",
    "1. 我们在邻域内每次都做一个随机选取，即总是从 $S_i$ 中随机抽取一个 $j$，作为下一步尝试的可行解。比如具体在 TSP 问题中，可以通过随机抽取 $p$ 和 $q$ 来进行 $2-$变换邻域内的随机抽取；\n",
    "2. 当存在邻域内的可行解 $j$ 满足 $f(j) > f(i)$ 时，也应该有一定概率用 $j$ 去代替$i$，也就是说应该保留一定概率让解往非局部最优的方向行走，这样才能留下脱离局部最优解的可能性；\n",
    "3. 在引入了上述随机搜索之后，原算法的终止判定不再适用，应该相应修改为若当前解 $i$ 在一个指定的步数 $N$（$N >> 1$）都不再变化时，算法终止。\n",
    "\n",
    "这几个问题，在 Metropolis-Hasting 抽样，一一对应都可以解决：\n",
    "1. 给出了实际的邻域选择；\n",
    "2. 我们这里可以假设路径长度在解空间服从 Boltzmann 分布，而引入温度 $T$ 来代表解的稳定程度；\n",
    "3. 就是 Markov 链达到了平稳分布。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kirkpatrick 在 1983 年将 Metropolis-Hasting 分布抽样方法引入了组合优化，并通过逐步降低温度来得到稳定的近似全局最优解，取得了不错的效果，这一方法被命名为**模拟退火法**。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**定理**  若组合优化问题 $(S, f)$ 的当前解服从平稳分布，则\n",
    "$$\n",
    "\\begin{equation}\n",
    "    \\lim_{t \\to 0}q_i(t) := q_i^* = \\frac{1}{|S_{\\mathrm{opt}}|}\\chi_{\\mathrm{opt}}.\n",
    "  \\end{equation}\n",
    "$$\n",
    "其中 $S_{\\mathrm{opt}}$ 表示最优解集合（不唯一），而 $\\chi_{\\mathrm{opt}}$ 则表示可行解$i$是最优解的特征函数：\n",
    "$$\n",
    "\\begin{equation}\n",
    "    S \\to \\{0, 1\\}, \\chi_{\\mathrm{opt}}(i) = \\left\\{\\begin{array}{ll}\n",
    "    1, & i \\in S_{\\mathrm{opt}},\\\\\n",
    "    0, &\\mbox{其它}.\n",
    "    \\end{array}\\right.\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "这个定理表明，如果每个 $t$ 至都能达到平稳分布，那么算法能收敛到全局最优解。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 冷却进度表\n",
    "\n",
    "在实际计算中，模拟退火法有几个重要参数需要决定：初始温度 $t_0$，终止温度 $t_f$，温度衰减函数 $t_k$，以及在每个温度的变换次数或 Markov 链长度 $L_k$。这一节我们面向\n",
    "具体问题来讨论如何确定这些参数。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**初始温度 $t_0$** 确定 $t_0$ 的基本出发点，从 Markov 链出发，我们希望 $t_0$ 基本上是一个无条件准平衡状态。也希望即初始接受率\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "  \\chi_0 = \\frac{\\mbox{接受变换数}}{\\mbox{提出变换数}} \\approx 1.\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "只有这样，我们才能在算法运行初期充分遍历整个可行解空间，发掘潜在的最优解。在这个前提下，根据Metropolis准则\n",
    "$$\n",
    "e^{-\\frac{\\Delta f}{t_0}} \\approx 1,\n",
    "$$\n",
    "知，$t_0$ 应取得较大。或者可以根据需要的 $\\chi_0$ 反向推导 $t_0$。比如如果知道 $\\Delta f$ 的上界为 $100$，且要求 $\\chi_0 = 0.9$，则可取 $t_0 > 949$。但如果缺乏对 $\\Delta f$ 的必要估计，那么也可以用具体的算法过程来控制，比如，Kirkpatrick 1982 提出，可以先确定一个初始 $t_0$，然后做几次尝试变换，若接受率不足，则将 $t_0$ 翻倍，如此循环直到 $t_0$ 满足要求。除此以外还有大量文献讨论这个问题。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**终止温度 $t_f$**\n",
    "一种暴力的做法是限制 $k$ (降温次数)的次数，比如 $k$ 至多 $50$ 次。这种限制主要来自硬件。而从理想角度出发，终止温度恰好和初始温度相反，我们希望它充分小。或者，接受率 $\\chi_f$ 充分小。为此可以分别设置阈值，当 $t_k$ 或 $\\chi_k$ 达到时，就终止算法。而一种更硬核的思路是在连续一个或若干个 Markov 链中，最优解都没有任何变 Kirkpatrick本人就持这种观点。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Markov链长度 $L_k$** 也即在一个 $t_k$ 温度下我们应该迭代多少次。理想的做法当然是迭代到平稳分布，或者至少利用局部信息监测到平稳分布的发生。但这样的算法往往是指数时\n",
    "间的。于是更常用的做法是设置一个多项式的上界 $\\bar{L}$，一旦达到，就不再在此温度继续尝试。比如对 TSP 问题，一个常用的上界是 $\\bar{L} = n^2$，这里 $n$ 指解空间规模 $|S|$ 。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**温度衰减函数 $t_k$** 一个最常用的衰减函数是\n",
    "$$\n",
    "\\begin{equation}\n",
    "  t_{k + 1} = \\alpha \\cdot t_k, k = 0, 1, \\cdots\n",
    "\\end{equation}\n",
    "$$\n",
    "其中 $\\alpha$ 接近 $1$，比如 $\\alpha = 0.95$。（别问为什么！）\n",
    "\n",
    "而稍微有节操一点的做法，比如\n",
    "$$\n",
    "\\begin{equation}\n",
    "  t_k = \\frac{K - k}{K} \\cdot t_0, k = 1, 2, \\cdots, K.\n",
    "\\end{equation}\n",
    "$$\n",
    "这个策略事实上和前面的有限步终止温度是配套的。\n",
    "\n",
    "这里再介绍一个在 TSP 问题中使用良好的降温函数：\n",
    "\n",
    "$$\n",
    "t_k = \\frac{c}{a + \\ln k}, k = 0, 1, 2, \\cdots, K.\n",
    "$$\n",
    "其中 $a$ 和 $c$ 是常数，$c$ 应当充分大以满足 $t_0$ 充分覆盖要求。这种负对数的取法，参考了熵的变化规律，因此在理论和实践中都有较好的表现。\n",
    "\n",
    "以上种种，都是开放问题，在每一个具体问题中，都需要基于上述思路去进行调整。目前在整个领域中，都没有明显的理论最优值可以提供。因此每年还在源源不断地产生大量的论文。大家如果在 SRTP 或者毕业设计中有需要，不妨也考虑一下，不过指导教师建议大家去找更专业的老师。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TSP 问题的代码实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "# 这句话是非标准的python，用于ipthon或jupyter这样的系统中，表示绘图即刻自动展开。\n",
    "%matplotlib inline\n",
    "\n",
    "# 这里把全部Warning过滤掉了. \n",
    "# 参见https://docs.python.org/2/library/warnings.html\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "from scipy import stats\n",
    "import numpy as np\n",
    "import sys\n",
    "import matplotlib.pyplot as plt\n",
    "#np.random.seed(250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def swapcities(cityXY):\n",
    "    n = cityXY.shape[1]\n",
    "    city = np.random.choice(n, 2, False)\n",
    "    city_1 = min(city)\n",
    "    city_2 = max(city)\n",
    "\n",
    "    s = np.hstack((cityXY[:,0: city_1], cityXY[:,city_2:city_1:-1], cityXY[:,city_1:city_1 + 1], cityXY[:,city_2 + 1:]))\n",
    "    # s = np.hstack((s, cityXY[:,city_1:city_1 + 1]))\n",
    "    # 这里使用了加一使得得到的矩阵的列宽为1，否则使用.shape会输出空的列宽，可以防止hstack报错 'dimention 不一致'\n",
    "    # s = np.hstack((s, cityXY[:,city_2 + 1:]))\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dis2(x, y):\n",
    "    # d0 = x[0] - y[0]\n",
    "    # d1 = x[1] - y[1]\n",
    "    # d = d0 * d0 + d1 * d1\n",
    "    # 原本已经是一个向量化的方法了，但还可以更简单,当x,y多维时输出一个多维的结果\n",
    "    return np.sqrt( (x-y)[0] * (x-y)[0] + (x-y)[1] * (x-y)[1]  )\n",
    "    # return np.sqrt(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def distance(cityXY):\n",
    "    dd = dis2(cityXY[:,:-1], cityXY[:, 1:])\n",
    "    d = np.sum(dd)\n",
    "    #使用向量化可以极大地提高计算速度\n",
    "    d += dis2(cityXY[:, -1], cityXY[:, 0])\n",
    "    return d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def TSPSA(cityXY, T0, MAXIT, N):\n",
    "    # 在有些不需要copy的地方，只传地址会更快\n",
    "    k = 0\n",
    "    t = T0\n",
    "    # x = cityXY.copy()\n",
    "    x = cityXY\n",
    "    dx = distance(x)\n",
    "    ds = dx\n",
    "\n",
    "    # n = x.shape[1]\n",
    "    # xs = x.copy()\n",
    "    # ds = distance(x)\n",
    "    # ds = dx.copy()\n",
    "    # 以上全部不需要做copy\n",
    "    for i in range(N):\n",
    "        while (k < MAXIT):\n",
    "            # dx = distance(x) # 原更新dx的方法\n",
    "            if (dx < ds):\n",
    "                xs = x\n",
    "                ds = dx\n",
    "            y = swapcities(x)\n",
    "            dy = distance(y)\n",
    "            h = min(1, np.exp(-(dy - dx)/t))\n",
    "            U = np.random.rand()\n",
    "            if (U < h):\n",
    "                # x = y.copy()\n",
    "                x = y\n",
    "                dx = dy # 这里优化了更新dx的方法\n",
    "            k = k + 1\n",
    "        # print(distance(x), t)\n",
    "        # t = t * a; 弃用的降温方法\n",
    "        t *= (1 - 1 / (50 + np.log(i + 1)))\n",
    "        k = 0\n",
    "        print(i, end=' ') # 打印以追踪进度\n",
    "    return xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plotcities(cityXY):\n",
    "    plt.figure()\n",
    "    plt.plot(cityXY[0, :], cityXY[1, :], 'b*')\n",
    "    plt.plot(cityXY[0, :], cityXY[1, :], 'b')\n",
    "    plt.plot([cityXY[0, -1:], cityXY[0, 0]], [cityXY[1, -1:], cityXY[1, 0]], 'b')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[0.03195598 0.35790338 0.87490239 0.98148435 0.22567331 0.89188455\n  0.43859297 0.67905994 0.88551619 0.82078562 0.73024472 0.45020836\n  0.30180855 0.31499125 0.7341481  0.34526016 0.45001029 0.21214625\n  0.02399456 0.88362404]\n [0.79949408 0.75426753 0.97721701 0.92275013 0.79032095 0.37579935\n  0.63999246 0.35842035 0.97600195 0.51860686 0.76046134 0.33454293\n  0.37670302 0.39139551 0.0478876  0.96525679 0.38403402 0.10751918\n  0.42221432 0.34922403]]\n"
     ]
    }
   ],
   "source": [
    "x = np.random.rand(2,20)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[0.03195598 0.35790338 0.87490239 0.98148435 0.22567331 0.89188455\n  0.43859297 0.34526016 0.7341481  0.31499125 0.30180855 0.45020836\n  0.73024472 0.82078562 0.88551619 0.67905994 0.45001029 0.21214625\n  0.02399456 0.88362404]\n [0.79949408 0.75426753 0.97721701 0.92275013 0.79032095 0.37579935\n  0.63999246 0.96525679 0.0478876  0.39139551 0.37670302 0.33454293\n  0.76046134 0.51860686 0.97600195 0.35842035 0.38403402 0.10751918\n  0.42221432 0.34922403]]\n"
     ]
    }
   ],
   "source": [
    "y = swapcities(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plotcities(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 "
     ]
    }
   ],
   "source": [
    "S = TSPSA(x, 20, 2000, 600)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plotcities(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.rand(2,300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x[0,:],x[1,:],'-b')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}